Correct me if I'm wrong, but my guess Burnfoot got killed by either being caught on fire, smoke inhalation, or by a tree/branch that fell on them because of the fire, or killed by a clanmate or another cat for causing the fire.
Those are a lot of guesses! lol
You were right with one though, Burnfoot got caught in a fire while they were being held prisoner by their leader who was trying to find out what to do with them. They were tucked in a tunnel, their guards ran away and trapped them.
The irony of it? They didn't set the fire that killed them.
There was a drought and WindClan had been experiencing tiny little brush fires because of the drought. This one just happened to be in camp.